Advanced Vitreous State – The Physical Properties of Glass Active Optical Properties of Glass Lecture 1: Fluorescence, Amplifiers and Lasers Denise Krol Department of Applied Science University of California, Davis Davis, CA 95616 dmkrol@ucdavis.edu dmkrol@ucdavis.edu Advanced Vitreous State - The Properties of Glass: Active Optical Properties of Glass 1
Active Optical Properties of Glass 1. Light emission Optical amplification and lasing (fluorescence, luminescence) Optical transitions, spontaneous emission, lifetime, line broadening, stimulated emission, population inversion, gain, amplification and lasing, laser materials, role of glass 2. Nonlinear Optical Properties Fundamentals: nonlinear polarization, 2nd-order nonlinearities, 3rd-order nonlinearities Applications: thermal poling, nonlinear index, pulse broadening, stimulated Raman effect, multiphoton ionization dmkrol@ucdavis.edu Advanced Vitreous State - The Properties of Glass: Active Optical Properties of Glass 2
Optical properties of materials (Lucas, lecture 16) • Four things can happen when light proceeds into a solid. I R I o • Part of the light can be reflected by the surface of the solid. Reflection I o I A • Part of the light can be absorbed by coupling into the solid. Absorption I S I o • Part of the light can be scattered by the atoms and defects in the solid. Scattering I o I T • Part of the light can be transmitted through the solid. Transmission • Therefore, for an incident beam of intensity I o entering the solid: I o =I R + I T + I A +I S
Optical transitions: absorption and emission E 2 An atom/ion in a material, such as glass, can absorb light, h ν = E 2 -E 1 ν is the frequency of light (photon) E 1 After absorption, the material does not stay in the excited state indefinitely, but it will go back to the ground state either by emitting light or giving off heat E 2 E 2 radiative decay non-radiative decay spontaneous emission E 1 E 1 dmkrol@ucdavis.edu Advanced Vitreous State - The Properties of Glass: Active Optical Properties of Glass 4
Spontaneous emission and lifetime E 2 There is a certain probability (A 21 ) for the atom to decay radiatively A 21 E 1 For a collection of N 2 atoms in the excited state: dN 2 dt = � A 21 N 2 With solution: � A 21 t = N 20 e � t / � τ is the lifetime N 2 = N 20 e Including non-radiative decay: A tot = A 21 + A nr τ = 1/A tot dmkrol@ucdavis.edu Advanced Vitreous State - The Properties of Glass: Active Optical Properties of Glass 5
Line broadening : homogeneous E 2 The finite lifetime of the excited state leads to a broadening of the emission linewidth: ν 0 =E 2 -E 1 /h E 1 I em Δν =A tot /2 π A tot /4 � 2 ( ) = I 0 I � 2 + A tot /4 � 2 ( ) ( ) � � � 0 ν - ν 0 The lineshape is Lorentzian and the same for all atoms homogeneous broadening dmkrol@ucdavis.edu Advanced Vitreous State - The Properties of Glass: Active Optical Properties of Glass 6
Line broadening : inhomogeneous There is also a broadening that results from the fact that not all atoms have the same surroundings (glass!) different atoms have slightly different transition frequencies The spread in frequencies is characterized by Δν INH � � � � 1/ 2 2 ( ) ( ) � � � 0 ( ) 2 ln2 exp � 4 ln2 � � ( ) = I 0 I � � � � � 2 � 1/ 2 � � INH ( ) � � � INH � � � � � � � I em Δν INH ν−ν 0 The resulting lineshape is Gaussian inhomogeneous broadening dmkrol@ucdavis.edu Advanced Vitreous State - The Properties of Glass: Active Optical Properties of Glass 7
Line broadening : homogeneous vs inhomogeneous Lorentzian Gaussian I em ν−ν 0 curves have same area and half-width dmkrol@ucdavis.edu Advanced Vitreous State - The Properties of Glass: Active Optical Properties of Glass 8
Glass: strong inhomogeneous broadening In general, one or the other line broadening mechanism can dominate In glasses -due to their disorder- inhomogeneous broadening almost always dominates From W.T. Silfvast, Laser Fundamentals, 2nd ed., Cambridge (2004) dmkrol@ucdavis.edu Advanced Vitreous State - The Properties of Glass: Active Optical Properties of Glass 9
Spontaneous vs stimulated emission E 2 E 2 E 2 ν 21 =E 2 -E 1 /h photon + E 1 E 1 E 1 spontaneous emission E 2 E 2 photon + + E 1 E 1 light amplification! stimulated emission dmkrol@ucdavis.edu Advanced Vitreous State - The Properties of Glass: Active Optical Properties of Glass 10
Stimulated emission vs absorption E 2 E 2 photon + + E 1 E 1 stimulated emission But we also have E 2 E 2 photon + E 1 E 1 absorption To have net amplification of light (gain) we need N 2 > N 1 We need population inversion dmkrol@ucdavis.edu Advanced Vitreous State - The Properties of Glass: Active Optical Properties of Glass 11
Population Inversion If there are only 2 levels inversion is not possible But if we have >3 levels inversion can be obtained Example: E 3 fast relaxation E 2 pump amplification (or laser) transition transition E 1 fast relaxation E 0 dmkrol@ucdavis.edu Advanced Vitreous State - The Properties of Glass: Active Optical Properties of Glass 12
Optical Amplification and Lasing gain amplifier medium ν 21 pump Because of stimulated process, amplified light has direction and phase of incoming signal laser = gain medium amplifier + optical cavity R=100% R=90% pump laser light has the following properties: • highly directional • highly monochromatic • highly coherent dmkrol@ucdavis.edu Advanced Vitreous State - The Properties of Glass: Active Optical Properties of Glass 13
Optical cavity modes L cavity axial mode frequencies ν = nc/2L axial mode separation Δν =c/2L dmkrol@ucdavis.edu Advanced Vitreous State - The Properties of Glass: Active Optical Properties of Glass 14
3-Level vs 4-Level Laser System E 3 E 3 E 2 pump laser E 2 transition transition pump laser transition E 1 transition E 1 E 0 3-level system 4-level system example : Er 3+ example : Nd 3+ In 3-level system more than 50% of level 1 needs to be pumped, so it is harder to obtain inversion: Pump and laser transition share a level dmkrol@ucdavis.edu Advanced Vitreous State - The Properties of Glass: Active Optical Properties of Glass 15
Some simple laser equations note: cw lasers! e 2 g th L = 1 gain =loss and ν = nc/2L R 2 g th = σΔ N th where σ is the emission cross-section (m 2 ). R = mirror reflectivity The lasing threshold is achieved when the pump rate (proportional to pump power) is high enough to obtain Δ N th . If the pump rate is increased further the steady state laser intensity (power/area), I ss , grows according to I ss = (P/P th -1)I sat Here P is the pump power, P th the pump power needed to reach threshold and I sat the saturation intensity (a fixed parameters for a given laser transition) dmkrol@ucdavis.edu Advanced Vitreous State - The Properties of Glass: Active Optical Properties of Glass 16
What makes a good laser transition/material? E 3 For cw operation: E 2 •Good pumping efficiency •Purely radiative lasing transition E 1 •Small difference between pump and laser wavelength E 0 •Fast relaxation from 3 ->2 and 1->0 Other important materials properties: •Thermal conductivity •Optical quality •Mechanical properties dmkrol@ucdavis.edu Advanced Vitreous State - The Properties of Glass: Active Optical Properties of Glass 17
Solid-state laser materials and glass Most solid state laser materials fall in one of 2 categories: 1. Dielectric materials (host material)doped with active ions: Nd 3+ :YAG, Cr 3+: Al 2 O 3 2. Semiconductor materials: GaAs, GaN transition-metal ions rare-earth ions (d-shell, broad transitions) (f-shell, narrow transitions) Cr 3+ Nd 3+ Ti 3+ Er 3+ Yb 3+ Host material influences emission and laser characteristics Glass is used as a host material dmkrol@ucdavis.edu Advanced Vitreous State - The Properties of Glass: Active Optical Properties of Glass 18
Nd-doped glass amplifiers Nd 3+ energy level diagram corresponding 4-level laser diagram for 1064 nm transition lasers crystals: narrow lines, better thermal conductivity glass: uniform & large pieces, broader lines, lower thermal conductivity amplifiers dmkrol@ucdavis.edu Advanced Vitreous State - The Properties of Glass: Active Optical Properties of Glass 19
Nd-doped glass amplifiers Phosphate glass preferred From W. Koechner, Solid State Laser Engineering dmkrol@ucdavis.edu Advanced Vitreous State - The Properties of Glass: Active Optical Properties of Glass 20
Erbium Doped Fiber Amplifier: EDFA Glass fibers: long interaction lengths, compact and robust 4 I 11/2 Energy levels of Er 3+ 4 I 13/2 Pumping bands @ 980 or 1480 980 nm nm 1520-1560 nm 1480 nm 4 I 15/2 Schematic diagram of EDFA dmkrol@ucdavis.edu Advanced Vitreous State - The Properties of Glass: Active Optical Properties of Glass 21
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